N.C. Gen. Stat. § 163-12

Whenever there shall be a vacancy in the office of United States Senator from this State, whether caused by death, resignation, or otherwise than by expiration of term, the Governor shall appoint to fill the vacancy until an election shall be held to fill the office. If the Senator was elected as the nominee of a political party, the Governor shall appoint from a list of three persons recommended by the State executive committee of the political party with which the vacating member was affiliated when elected if that party executive committee makes recommendations within 30 days of the occurrence of the vacancy. The Governor shall issue a writ for the election of a Senator to be held at the time of the first election for members of the General Assembly that is held more than 60 days after the vacancy occurs. The person elected shall hold the office for the remainder of the unexpired term. The election shall take effect from the date of the canvassing of the returns.